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Metal laser cutting belongs to mature laser material processing technologies in industry applications. However, without understanding of the mechanism underlying the overall process, the improvement of the cutting quality is restricted. In this paper, an instantaneous melt removal model is presented to describe the process of material removal and striation formation. In the temperature field calculation, melted metal layer is removed when it grows to an assumed thickness. The effects of cutting parameters including cutting speed, gas pressure and laser power on the shape of striation are discussed. A novel method of getting striation free cutting surface is presented. Finally, laser cutting experiments of mild steel is conducted to validate the model. The striation variation trend can be well predicted by the model presented here and the disagreement may be caused by the coupling effect of cutting speed and critical thickness value.

Laser processing technology has been used in industry with the properties of non-contact, high brightness, coherence and monochromaticity. Of the applied technologies, laser cutting is widely used with the features of high efficiency, small heat-affected zone and good cutting quality. However, on the resulting cutting surface, periodic distributed striation often exists along the cutting direction, which induces poor laser cutting quality. Laser cutting of metal sheet is often used for the blanking of butt welding process. Because of the striations, the weld strength is dramatically reduced.

There are generally three kinds of striation distributed on the cutting surface [

In this paper, the melt film formation and varying power absorption under laser irradiation are both considered in a dynamic process. The melted layer adhering to the cutting front is removed at a critical thickness S_{0}. Then a one dimensional model was established to predict the depth and wavelength of striation. The model characterizes the correlation between the process parameters and striation geometry, while providing the guidelines in obtaining striation-free cutting surface in laser cutting application. Finally, sheet metal cutting experiments were performed.

The workpiece is fixed with the moving laser incidence absorbed on the cutting front. The multiphase flow model (assisting gas flow, melt and solid metal) is simulated with the volume fluid method in FLUENT. The schematic of melt formation and removal is shown in _{m}, the melting front grows along the laser beam scanning direction and the thickness of the melting layer (red part) increases. When the thickness reaches the critical value S_{0}, the melt is assumed to be removed instantaneously. The parameter S_{0} is the maximal thickness melt film layer can increase to before it is removed. It should be result of the balance among the recoil pressure, surface tension, and assisted gas pressure.

In the instantaneous removal model, the heat transfer problem involved is the temperature variation of the cutting front caused by varying distances between the cutting front and the centerline of the laser beam. In the calculation, the laser heat source adopts TM_{0} mode (i.e. Gaussian power distribution). The heat absorbed by the metal is usually characterized by the absorption coefficient A_{0}, which is determined by surface topography, incident angle, laser polarization, temperature and so on. It is assumed to be constant in the formulation. The intensity in the coordinate is depicted as

I 0 ( x ) = 2 P L A 0 π w 0 2 e − 2 ( x − x 0 ) 2 w 0 2 (1)

where P_{L} is the laser power, X_{0} is the laser beam center and W_{0} is the focused laser radius.

The heat equation is as follows:

∂ T ( x , t ) ∂ t − α ∂ 2 T ( x , t ) ∂ x 2 = 0 , x = ( 0 , + ∞ ) (2)

where α is the thermal diffusion coefficient.

As for the boundary conditions, there are two cases to be considered. When the temperature of the heating front T(X_{b}, t) is less than the melting temperature Tm, the cutting front is in the heating stage.

I 0 ( | x b − x 0 | ) + k ∂ T ∂ x | x = x b = 0 , T ( x b , t ) < T m (3)

where X_{b} is the heating front and k is the thermal conductivity.

When T(X_{b}, t) is equal to T_{m}, the melting front X_{m} moves to the positive direction of the x axis at the melting speed. V_{0} is the cutting speed.

I 0 ( | x b − x 0 | ) + λ ∂ T ∂ x | x = x m = ρ L x m ( t ) . , T ( x m , t ) = T m (4)

where X_{m} is the melting front, L is the latent heat of melting, ρ is the density of melt.

The heat equation is resolved in a semi-infinite solid and the infinite boundary condition is

T ( ∞ , t ) = T a (5)

The laser power is absorbed at the heating front X_{b} to move the melting front X_{m} forward. The relation between these two fronts is

x b = int ( x m s 0 ) ⋅ s 0 , s 0 ≠ 0 x b = x m , s 0 = 0 (6)

where S_{0} is an empirical value which should be in proportional to the striation depth. The usual experiment striation depth lies in 30 - 80 μm. Divided by the laser spot (110 μm), this dimensionless parameter is equal to 0.5 for typical cutting parameters in the model.

The variables in the equations above have different dimensions. For the convenience of numerical calculation, three dimensionless variables temperature θ, length ξ, time t and three dimensionless constants, Peclet number P_{e}, laser power P_{A}, and inverse Stefan number are introduced to acquire dimensionless formulations.

θ = T − T a T m − T a , ξ = x w 0 , τ = α w 0 2 t P e = w 0 v 0 α , P A = 2 P L A 0 π w 0 k ( T m − T a ) , S t ′ = L c ( T m − T a ) (7)

where P_{e} is the ratio of the advective transport rate to the diffusive transport rate, and S t ′ is the ration of the latent heat to the sensible heat.

When it comes to the melting stage, the heat transfer happens in a moving melting boundary, i.e. the Stefan problem. A transformation is introduced as follows:

y = 1 1 + ξ − ξ m ( τ ) (8)

The Equations (2)-(5) are then transformed into

∂ θ ∂ τ + y 2 ξ m ( τ ) · ∂ θ ∂ y = 2 y 3 ∂ θ ∂ y + y 4 ∂ 2 θ ∂ y 2 (9)

P A e − 2 ( ξ b − P e τ − ξ 0 ) 2 − ∂ θ ∂ y | y = 1 = 0 , θ ( 1 , τ ) < 1 (10)

P A e − 2 ( ξ b − P e τ − ξ 0 ) 2 − ∂ θ ∂ y | y = 1 = S t ⋅ ξ m ( τ ) · , θ ( 1 , τ ) = 1 (11)

θ ( 0 , τ ) = 0 (12)

The Equations (9)-(12) are resolved using the finite difference method (FDM) in Mathematica^{®}.

The temperature field in the metal is shown in _{0} is equal to 0. The difference between the heating state and the melting state is the temperature at the melting front y = 1. In the steady state and the melting state, the temperatures at the melting front are all held to be the melting point T_{m}, while the temperature here is a little low in the heating state. From the temperature distribution, it can be seen that the temperature in the melting state in the region 0 < y < 1 is lower than that in the steady state. The reason is that the melting speed in the melting state is bigger, and more energy is used to melt the metal.

_{0}, the melt is removed instantaneously and the heating front moves forward in a step.

The distance between the melting front and the center of the laser beam determines the energy absorption rate in melting the metal. And in the cutting process, its variation is cyclic as shown in

characterized distance reflects the phase transition boundary, i.e. the shape of striation.

As shown in _{0}, the higher cutting speed means faster energy input rate and smaller temperature variation at the cutting front.

As shown in _{0}, the amplitude and wavelength of the striation grow. Obviously, the effect of S_{0} has a contrary trend compared with that of P_{e}. S_{0} is influenced by the assisted gas flow and the dimensionless P_{e}, which reflects the heat input.

In _{A} has little impact on the shape of striation. But another

result which should be concerned is that the mean value of the distance increases with a bigger P_{A}. For a fixed cutting speed, the power absorbed by the heating front is almost constant in the steady cutting process. As a result, if the simulative laser power P_{A} increases, it is reasonable that the distance between the laser center and the cutting front is bigger. Back to the analysis in Section 3.1 and 3.2, mean value of the distance decreases when P_{e} increases with a bigger S_{0}.

Through the parameter analysis above, the variation trend of striation is obtained. Based on the inspiring result, striation suppression strategy is presented according to the instantaneous melt removal model. In the model, variation of the distance is used to approximately represent the shape of striation. When this value is kept constant, the formation and removal of melt layer become continuous without heating stage. Then the striation free condition is built. The laser power directly affects the melting speed. Therefore, the modulation of laser power will directly control this variation, while suppressing the formation of striation.

Assuming that P_{A} is the temporal function, i.e. P_{A} = P_{A}(τ) and the melting speed is equal to the cutting speed. The time dependent laser power is obtained as

P A ( τ ) = P e ( 1 + S t ′ ) ⋅ e 2 ( I n t e g e r P a r t ( 1 + P e τ s 0 ) × s 0 − P e ⋅ τ − ξ 0 ) 2 (13)

This is the exponential distribution as shown in

The experiment of mild steel laser cutting was conducted to validate the model. Rofin DC030 CO_{2} laser with a conical nozzle is adopted. The laser power was 3000 W and nitrogen was used as the assisting gas. The mild steel was Q235-A. The cutting parameters are listed in

Cutting parameters | Laser power p_{L} (W) | 3000 | Cutting velocity (m/min) | 1 - 5 | Spot diameter w_{0} (μm) | 110 |
---|---|---|---|---|---|---|

Q235-A | specific heat c (J/kg×K) | 482 | thermal conductivity k (W/m×K) | 59.5 | Melting temperature T_{m} (K) | 1753 |

Density ρ (kg/m^{3}) | 7860 | Fusion latent L (kJ/kg) | 272 | Ambient temperature T_{a} (K) | 293 | |

Dimensionless parameters | power P_{A} | 60 | velocity P_{e} | 0.153 - 0.764 | latent St | 0.39 |

melt removal by the gas flow. The circular cavity is the melt melting result of the laser heat source. And the tips between the cavities are formed by the melt removal. The amplitude A and the wavelength λ of the striation are measured to evaluate the striation in the following discussion. Striations on the resulting surface in the experiments show different morphology at increasing cutting speed as shown in

are underestimated. This discrepancy could be come from the difference between the real melt lay thickness and the critical thickness S_{0} which is assumed to be 0.5. The parameter also depends on the varying cutting velocity. However, even increasing the cutting speed until the metal couldn’t be cut through, the striation free cutting surfaces weren’t obtained.

The striation suppression strategy: exponential power modulation requires the laser power to be reduced by hundreds of watts in one millisecond that exceeds the operating range of the controller. Although the validation experiments aren’t performed, the relation between the striation elimination and laser power modulation is clearly seen.

The formation of striation on the cutting surface is determined by the evolution and the removal of the liquid melt layer. The presented instantaneous melt removal model predicts the variation trend of the wavelength and the amplitude of the striation, so that striation-free cutting surface is possible to be obtained by appropriate cutting strategy. Based on the above model, a striation suppression strategy based on the laser power modulation is presented. However, power modulation on laser cutting machine now is very hard to be realized, and this modulation method deserves further study. The results obtained are summarized as follows:

1) Laser cutting mechanism consists of heating stage and melting stage. The discontinuous melting process because of the existence of heat stage is the cause of wavelike striation.

2) Laser cutting parameters have an important impact on the shape of striation. The increase of cutting speed contributes to striation suppression.

3) The laser power exponential temporal distribution eliminates the striation theoretically derived by the model. Further experiments are needed to verify this cutting strategy.

Li, C. and You, D.F. (2018) Analysis of Striation Formation and Suppression Strategy on Upper Edge of Cutting Surface in Laser Cutting. World Journal of Engineering and Technology, 6, 201-213. https://doi.org/10.4236/wjet.2018.61011